Selecting Verts I dont want
Using the box-select tool [b] in edit mode adds to the selection. That unwanted point was part of your previous selection. You can remove this by simply holding down [shift] and right clicking the unwanted vertex. 

Whenever you want to make a new selection using the box-select, remember to first de-select everything by pressing the [a] key. The box-select tool shouldn't make any selections outside of its influence area.